The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).

Answers

Answer 1

Answer:

Vertex form is f(t) = 4 [tex](t-1)^{2}[/tex] +3 and vertex is (1, 3).

Step-by-step explanation:

It is given that f(t)= 4 [tex]t^{2}[/tex] -8 t+7

Let's use completing square method to rewrite it in vertex form.

Subtract both sides 7

f(t)-7 = 4 [tex]t^{2}[/tex] -8t

Factor the 4 on the right side.

f(t) -7 = 4( [tex]t^{2}[/tex] - 2 t)

Now, let's find the third term using formula [tex](\frac{b}{2} )^{2}[/tex]

Where 'b' is coefficient of 't' term here.

So, b=-2

Find third term using the formula,

[tex](\frac{-2}{2} )^{2}[/tex] which is equal to 1.

So, add 1 within the parentheses. It is same as adding  4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.

So, we get

f(t) -7 +4 = 4( [tex]t^{2}[/tex] -2 t +1)

We can factor the right side as,

f(t) -3 = 4 [tex](t-1)^{2}[/tex]

Add both sides 3.

f(t) = 4[tex](t-1)^{2}[/tex] +3

This is the vertex form.

So, vertex is (1, 3)


Related Questions

The value of -9 is __ than the value of -12 because -9 is to the __of -12 on the number line.


Less

Or
Greater

Answers

Answer:

Step-by-step explanation:

-9 is greater than the value of -12 because -9 is to the right of -12 on the number line.

If 'a' is a number lying between 0 and 1. then which of the following is in increasing order? a) a², a, √a b) a √a ,a² c) a²,√a,a d) a, a², √a ​

Answers

Hello,

[tex]0\leq a\leq 1 \Longrightarrow 0*a\leq a*a\leq 1*a \Longrightarrow 0 \leq a^2 \leq a\\\\0\leq a^2\leq a \Longrightarrow \sqrt{0} \leq \sqrt{a^2} \leq \sqrt{a} \\\\The\ function\ y=x^2\ is\ increasing\\\\Answer A\\\\ex: a=0.5 \\\\a^2=0.25\\\\\sqrt{a}=\dfrac{\sqrt{2}}{2}\approx{0.7071...}\\\\and\ 0.25\leq 0.5 \leq 0.7071...[/tex]

Surface Area of Prisms
Can someone show me how to solve and also what the formula is. Please!​

Answers

Answer:

400 in.²

Step-by-step explanation:

Surface area of the triangular prism = bh + L(s1 + s2 + s3)

Where,

b = 8 in.

h = 15 in.

s1 = 17 in.

s2 = 15 in.

s3 = 8 in.

L = 7 in.

Plug in the values

S.A = 8*15 + 7(17 + 15 + 8)

S.A = 120 + 7(40)

S.A = 120 + 280

S.A = 400 in.²

(14) (55, 42, 32, 48, 55, x), mean = 49

Answers

Answer:

78

Step-by-step explanation:

Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done

what is the proportion 4/y= 5/10

Answers

Answer:

So, y =8

Step-by-step explanation:

4/y = 5/10

or, 4*10 = 5*y

or, 40 = 5y

or, y = 40/5

therefore, y = 8

I have no idea how to do this, it is due in two days. Hopefully someone sees this before then.

Answers

Hello,

[tex]m\ \widehat{ABC}=x\\m\ \widehat{BAC}=2*x\\\\So:\\ x+2x=90^o\\x=30^o\\[/tex]

[tex]cos(30^o)=\dfrac{\sqrt{3} }{2} \\[/tex]

In the triangle ABC,

[tex]cos(30^o)=\frac{BC}{BA} \\\\BA=\dfrac{cos(30^o)}{BC} \\\\BA=\frac{\dfrac{\sqrt{3} }{2} }{24} =16*\sqrt{3} \\\\[/tex]

[tex]sin(30^o)=\dfrac{1 }{2} =\dfrac{AC}{AB} \\\\AC=\dfrac{1}{2} *16\sqrt{3} =8\sqrt{3}[/tex]

In the triangle ACB,

[tex]cos(30^o)=\dfrac{AC}{AL} \\\\AL=\dfrac{8\sqrt{3} *2}{\sqrt{3} } =16\\[/tex]

685 gym members were asked if they use the elliptical machine or treadmill as their primary cardiovascular exercise. 257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.

a.) Organize this using a venn diagram (2 marks)

b.) A gym member is chosen from this group. What is the probability that this member uses the treadmill only? (1 mark)

Answers

Given:

Total number of gym members = 685

257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.

To find:

a. The venn diagram.

b. The probability that a member uses the treadmill only?

Solution:

(a)

We have,

Total number of gym members = 685

Treadmill user = 257

Elliptical user = 157

Who use both = 85

Only treadmill user is:

[tex]257-85=172[/tex]

Only Elliptical used

[tex]157-85=72[/tex]

Therefore, the venn diagram for the given situation is shown below.

(b)

The member who use treadmill only = 172

Total user = 685

The probability that a member uses the treadmill only is:

[tex]P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}[/tex]

[tex]P(\text{Only treadmill})=\dfrac{172}{685}[/tex]

Therefore, the probability that a member uses the treadmill only is [tex]\dfrac{172}{685}[/tex].

A retailer allows 15% discount on the Marked price of an electric fan. If a customer pays Rs 2244 with 10% VAT,find the Marked Price of the fan​

Answers

Answer:

2400

Step-by-step explanation:

2244 is the final price. it includes the VAT based on the actual sale price. and that is then actually 15% lower than the originally marked price.

so, let's calculate backwards :

2244 = 100% sale price + 10% VAT = 110%

1% = 2244 / 110 = 20.40

100% (actual sale price) = 20.40×100 = 2040

now, because of the 15% discount, these 2040 are only 85% of the originally marked price.

2040 = 85%

1% = 2040 / 85 = 24.00

100% (the original marked price) = 24×100 = 2400

How do I simplify rational expressions

Answers

Answer:

a rational expression is an expression that has a RATIO in it

look at the word "RATIO"nal

a ratio is just a fraction...

so your question is "how to simplify fractions"

lots of approaches, this is one of them...

PRIME FACTOR the numerator and denominator

[tex]\frac{90}{135}[/tex]

90 = 2 * 3 * 3 * 5

135 = 3 * 3 * 3 * 5

= 2/3 (the two 3's cancel and the 5's cancel)

Step-by-step explanation:

Express sin O as a fraction in simplest form

Answers

Answer:

sin o = opposite/hypotenuse

sin o= 7/12

Duke works on commission basis. He gets 20% of his total sales. If he
earned $55 last week, what were his sales for the week?

Answers

Answer:

$275

Step-by-step explanation:

Find his sales by dividing 55 by 0.2:

55/0.2

= 275

So, his sales for the week were $275

what is 50000000000000000000000000000 cubed

Answers

Answer:

50000000000000000000000000000*50000000000000000000000000000*50000000000000000000000000000=1.25e+86

Hope This Helps!!!

Solve. Algebra 1
14=4-6x-2

Answers

Answer:

Step-by-step explanation:

resolver. Álgebra 1

14=4-6x-2

4-6x-2 : 2

Rpta: 2

Is (-4, 2) a solution of 4x + 5y <_-7?
Choose 1 answer:
Yes or No

Answers

Answer:

no

Step-by-step explanation:

substitute the (x,y) values into the inequality.

4(-4)+5(2) less than or equal to -7

-16+10≤-7

-6≤-7 not a valid answer so ((-4,2) is not a solution

3. Find the products using suitable identity:
a) (t –2)(t –2) b) (3y –2z) (3y + 2z) c) 105 × 98v

Answers

Answer:

a) t²- 4x + 4

b) 9y² - 4z

c) 10290v

Step-by-step explanation:

a+b) use identity (ax+b)(ax+c) = ax² + (b+c)x + bc

c) a × bx = abx

Help me please and thank you.

Answers

Answer:

[tex]0.67x-2=0.43[/tex]

Step-by-step explanation:

2/3 = 0.6 repeating

3/7 = 0.42857

pls help me expand this expression

Answers

Answer:

just be smart

Step-by-step explanation: (2x)

Please help me with this one

Answers

Answer:

71.51

Step-by-step explanation:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=3·3+7·3+7·3+1

2·﹣34+2·(3·7)2+2·(3·7)2﹣74+2·(7·7)2﹣74=71.51219

Gente por favor ayuda tengo que presentarlo hoy:(

Answers

Answer:

english pls :c

Step-by-step explanation:

The first and last term of an A. P are 1 and 121 respectively. Find the number of terms in the A.P and the common difference between them if the sum of the term is 1281​

Answers

Answer:

No.of terms=21

Common difference=6

Which operation will solve the following word problem? Jeff earns $14.00 per hour, Tom earns half as much as Jeff. How much does Tom earn per hour?


a.) Multiplication


b.) Subtraction


c.) Addition


d.) Division

Answers

Answer:

Multiplication

Amount Tom earns per hour = $7

Step-by-step explanation:

Amount Jeff earns per hour = $14

Amount Tom earns per hour = 1/2 × $14

Note: 1/2 = 0.5

Amount Tom earns per hour = 1/2

× $14

= 0.5 × $14

= $7

Amount Tom earns per hour = $7

Which expressions have the same solution as –4(6)? Select three options..
–4(– 6)
4(– 6)
6(– 4)
–8(2)
12(– 2)

Answers

4(-6)
6(-4)
those 2 have the same solution as -4(6)

Answer:

4(– 6)

6(– 4)

12(– 2)

Step-by-step explanation:

A triangle is rotated 90 about the origin. Which rule describes the transformation?

Answers

Answer:

1st option

Step-by-step explanation:

Under a rotation about the origin of 90°

a point (x, y ) → (- x, - y )

Answer:

your answer will be the first option

Step-by-step explanation:

edge 2021

What is the length of leg s of the triangle below?
45
4-12
90°
45

Answers

Answer:

A

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

s × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

s = 4 → A

Select the correct answer. Help

Answers

I believe it’s B not sure tho

WILL MARK BRAINLIEST

Please help solve problems with common tangents.

Answers

Answer:

not sure, sorry : p

Step-by-step explanation:

If you flip a penny, toss a 1–6 number cube, and flip a quarter, how many outcomes are possible?

Answers

Answer:

6x 2 = 12

Step-by-step explanation:

Answer:

24

EXPLANATION:

there's 4 different outcomes for the Penny and Quarter combos

- P Heads and Q Heads

- P Tails and Q Heads

- P Heads and Q Tails

- P Tails and Q Tails

Each of those outcomes will have one of six numbers so I just figured

6 outcomes for number cube × 4 outcomes for P and Q (penny and quarter)

6 × 4 = 24

:)

Could anyone help me solve for x? I've tried multiple times and can't seem to get the answer that was given

Answers

Step-by-step explanation:

Try Photo-math app or Math-way app.

Find the area of circle x that has a radius at coordinates X = (0, 3) and Y = (-3, -1). Round to the nearest tenth.

Answers

Answer:

78.5 units²

Step-by-step explanation:

Area of circle:

A = πr²

Distance between x and y is same as r, so:

r² = (0 + 3)² + (3 + 1)² = 9 + 16 = 25

Then the area is:

A = π*25 = 78.5 units² (rounded)

Can someone please help me with this question

Answers

Answer:

The answer should be: B

I think it's B because there are 2 cups of water (2c) and 7 bottles of water (7w) which costs $16 so that would be 2c +7w=16. Also for the other one, it's 3 cups (3c) and 8 bottles of water (8W) and the cost is $19 so that would be

3c + 8w =19

Step-by-step explanation: Hope this helps and gl :))

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